The present invention refers to the creation of numerical models representing tridimensional actual models. The invention was developed with particular reference to the creation of models of tridimensional surfaces. One particular application sector of the invention refers to the creation of numerical models of surfaces by means of the acquisition of points from a tridimensional actual model.
In particular, although not exclusively, the invention was developed to be applied to technical sectors which require computer processing of numerical or mathematical models of so-called xe2x80x9csculpturedxe2x80x9d surfaces, such as for example those of motor vehicle body parts, of fairings, of shaped paneling, of casings for electrical appliances, of articles in the sector of design or ornamental models, of protective guards for machines or motors, which cannot be identified as union or development of elementary or primitive surfaces.
The known methods for the creation of numerical models of sculptured surfaces mainly use acquisition systems comprising continuous probes which explore the characteristics of the surface of a tridimensional actual model, providing an enormous mass of output data which represent the spatial coordinates of an equally high number of separate points of the surface of the model. This enormous amount of information is then processed by a computer programmed to provide output data which represent the shape of the surface of the actual model and which can be subsequently used by designers for any kind of analysis, calculation, modification or electronic processing of the characteristics of the surface itself. For example, the numerical or mathematical model of the surface can be used as input data for programs which calculate the resistance to certain types of stress, for Computer Aided Design (CAD) programs or for Computer Aided Manufacturing (CAM) programs and the like. The principle on which the above type of known systems is based is that the closer the points measured on the surface of the actual model are to each other, the more faithful the numerical reconstruction of a model with this surface will be. The utmost development of this principle has led to the production of increasingly sophisticated measuring instruments, which are able to supply the computer with the data of so-called xe2x80x9cpoint cloudsxe2x80x9d to emphasize the high surface unit density.
However, the above-mentioned known systems for the creation of numerical models of sculptured surfaces encounter obvious limitations in defining numerical models of surfaces which must be subsequently processed electronically. The processing programs are in fact generally designed for the input of a much lower quantity of data than is generated by the known xe2x80x9cpoint cloudxe2x80x9d measurement systems. In many of these programs, moreover, the input points represent the same number of xe2x80x9cnodesxe2x80x9d of the mathematical model, on which also rather complex calculations are made and whose relative position also significantly affects the output results. This aspect is well known to expert technicians involved in structure resistance calculations, for whom the preliminary task of identifying the nodes, the so-called xe2x80x9cmeshingxe2x80x9d phase of the model, often takes priority with respect to the actual calculation phase since an incorrect selection of the nodes can lead to totally unreliable results. A similar problem is encountered by designers who use CAD programs, who often find it difficult, if not impossible, to electronically handle surfaces identified by Incorrectly selected parameters or nodes. The modification, stretching or junction of bad numerical models of surfaces can lead to unforeseeable results, such as an unforeseen discontinuity in modified modeled surfaces, which are usually difficult to correct.
Furthermore, an additional disadvantage of the known procedures for the creation of numerical models derives from the fact that to obtain a surface model that can be easily processed by the programs used by designers, the data of the xe2x80x9cpoint cloudsxe2x80x9d must be processed by the application of algorithms which provide a reduced number of numerical parameters representing the shape of the surface of the actual model. While it is fairly simple to realize at a glance that the sculptured surfaces of actual models have a generally harmonic development and are well joined together, it is extremely difficult to design a good program which can identify, select or calculate precisely those nodal points from the enormous quantity of data from the xe2x80x9cpoint cloudsxe2x80x9d which can effectively represent the shape of these surfaces. Minor errors in the data of a few points of all those acquired can propagate without control in the calculation of numerical models of surfaces, without taking into account the fact that, due to the large quantity of input data, this calculation may prove to be long and costly and require calculation power that is often not available.
One radically different system with respect to the processing of point clouds for the mathematical representation of actual models is described in the document U.S. Pat. No. 4,979,224. According to this known system, the surface of the article which must be modeled is divided into one or more areas and an acquisition machine is operated to acquire the measurement of points along the boundaries of the areas with a certain degree of precision. The boundaries are mathematically modeled by means of algorithms and equations which minimize the deviation from the measured points. The surface of each area on the actual article is then measured at selected points and the values are compared to the values derived from the modeling equations at the same points and the equations are modified to minimize the deviation of the model from the measured points. The procedure is repeated by means of subsequent iterations until the required degree of surface modeling accuracy is achieved.
One disadvantage of this known system consists of the fact that there is no guarantee that the iterative procedure converges towards a mathematical surface model that, at each subsequent iteration, becomes more similar to the actual surface. Another disadvantage consists of the fact that the calculation of the minimum deviation of the model compared with the measured points implies the resolution of equation systems that, iteration after iteration, are of higher orders, meaning that the procedure must inevitably be interrupted when the available calculation power is no longer sufficient, regardless of the accuracy achieved. In addition, the complexity of the calculations necessary to model complex surfaces requires the adoption of powerful and expensive computers and the use of processing times which can be considerable.
The continuous probes used in the known type systems can be the contact type or the non-contact type, for example laser probes. These latter probes emit a beam of electromagnetic waves, in particular a beam of laser light, along a predetermined axial direction and, by means of a receiver, can detect the spatial position of a point on the surface of the object on which the electromagnetic waves are reflected.
A first known type of laser probe, which will be identified subsequently with the term xe2x80x9cmeasurement band typexe2x80x9d, transmits an analogue or digital output signal proportional to the distance of the point on the surface from the probe along the predetermined axial direction.
As shown in FIG. 3, in the known acquisition systems using laser probes of the above-mentioned first type, one or more probes 12 are translated along a direction X1 at a predetermined distance from an object O whose outline is to be detected, in such a way that the furthermost Z0 and the closest point Z1 of the object are included in the measurement band D of the probe, which sends an analogue or digital output signal, proportional to the distance of the outline of the object O along the predetermined measurement axis Z, to a processing system.
The known type of measuring systems mentioned above using measurement band type laser probes have the disadvantage of being difficult to use when the object to be measured has a highly complex surface. In such cases, it is in fact necessary to use probes with a very wide measurement band, implying high costs and low measuring precision. In certain cases, moreover, probes with sufficiently wide bands may not even be available.
An alternative system for detecting points on the surface of a tridimensional object uses the second type of laser probes, which we shall subsequently define as xe2x80x9cfixed focus typexe2x80x9d or fixed measurement point-type, whose behaviour in terms of acquisition operations, is fully comparable to the one of standard mechanical probes, the only difference being that there is no contact with the surface of the object when the measurement is made.
The path followed by a probe of this second type fitted on known types of measuring machines is very similar to that of a mechanical probe:
rapid approach towards the object according to a substantially perpendicular direction with respect to its surface at the point to be acquired,
slowed-down precision approach until the focusing point is reached,
transmission of a trigger signal to a control device connected to the laser probe,
withdrawal of the sensor perpendicular to the surface of the object,
movement of the sensor to a different point on the surface of the object.
The steps listed above involve a notable outlay of time in the process of acquiring the surface data of an object due to the periods of inactivity which cannot be used for the acquisition of points, but which are necessary for the approach and withdrawal of the probe towards and away from the surface of the object.
The object of this invention is to overcome the shortcomings of the known art, providing a method for the creation or generation of numerical models of surfaces, and in particular of sculptured surfaces, which is simple and economical to carry out and which at the same time ensures a high degree of reliability of the resulting model, limiting the number of points acquired on the actual model, so as to simplify and speed up the step of point acquisition which can be carried out by means of relatively inexpensive systems.
Another object of the invention is to provide a system for the creation or generation of numerical models of tridimensional surfaces which is precise, economical and quick and easy to carry out.
In order to achieve these objects, the subject of the invention is a method of the type indicated in the preamble of this description, comprising the steps of:
a) identifying at least one boundary on the surface of the actual model;
b) identifying a first plurality of points on the at least one boundary;
c) acquiring the values of the spatial coordinates of the first plurality of points by means of an acquisition system;
d) generating a first numerical representation of at least one theoretical surface having at least one boundary defined by the values of the spatial coordinates of the first plurality of points;
e) determining values representing a second plurality of nodal points belonging to the at least one theoretical surface;
f) operating the acquisition system to acquire the values of the spatial coordinates of a third plurality of actual points, directing the acquisition system towards the estimated positions of the nodal points of the second plurality;
g) generating a second numerical representation of at least one theoretical surface which satisfies the condition of at least passing through the points of the third plurality.
One advantage of the invention consists of the fact that the use of traditional type, generally expensive, continuous type probes is not necessary for the step of acquiring the points on the surface of the actual model, even though the method can also be applied advantageously to the point clouds acquired according to traditional systems so as to safeguard existing installed systems while ensuring the rapid and reliable generation of numerical models in a format suitable for subsequent processing with CAD programs, structural calculation programs or for the operation of numerical control equipment and machines.
In other words, in one of its embodiments, the system of this invention can be used in association with the known acquisition systems of xe2x80x9cpoint cloudsxe2x80x9d. In another of its forms, the system of the present invention involves the use of non-contact laser and similar type probes, both the measurement band type and the single point acquisition type. In an additional embodiment, the system uses acquisition machines with traditional mechanical probes.
Another advantage consists of the fact that the invention makes it possible to provide numerical models of surfaces also starting from actual surfaces that present discontinuities such as holes, cuts, superficial defects, sharp edges, tips and the like. In this way it is possible to generate numerical models also starting from the data of points acquired on the surface of complex, defective or imperfect quality actual objects, ensuring nevertheless a good definition of the numerical model of the surface.
If non-contact measurement band type probes are used, the system according to this invention makes it possible to eliminate the approach and withdrawal steps of the traditional probe towards and away from the surface of the object according to the directions perpendicular to it since these probes, fitted on measuring machines designed for continuous orientation of the probe, can xe2x80x9csweepxe2x80x9d the actual surface of the object, following its shape thanks to the definition of the theoretical surface and of its theoretical perpendiculars, to acquire the coordinates of the actual points in correspondence with positions predefined by the theoretical points.
To obviate the need to provide measuring machines that can continuously orientate a probe on a continuous basis, certainly much more expensive and more difficult to find on the market with respect to traditional measuring machines, it is however possible to exploit the characteristics of non-contact type sensors, either measurement band type or single point acquisition type, to make the acquisition of points from the actual model faster then the known type of systems. In the known systems using contact probes, in fact, after the probe has approached the surface of the actual model and the coordinates of an actual point have been acquired, it is necessary to withdraw the probe from the surface of the model before it can be moved towards another point for the acquisition of the relative coordinates, in order to prevent mechanical interference of the probe with the surface of the model. The system of this invention, on the contrary, allows the probe to approach the surface of the actual model, acquire the point and subsequently proceed for a distance along the perpendicular, virtually xe2x80x9cbreaking downxe2x80x9d the surface of the model, to move towards the next point, which will be acquired with a movement of the probe always along the perpendicular direction with respect to the surface of the model, but with a xe2x80x9cwithdrawingxe2x80x9d movement from the surface. The resulting overall path of the probe is certainly shorter than that normally used in the known systems, and, during the experimental tests carried out by the applicant, made it possible to significantly reduce the acquisition times of the points of an actual tridimensional model and the consequent generation of a model of the surface of this model.
Compared with known acquisition systems using measurement band probes, a particular embodiment of the invention using this type of probe has the advantage of requiring less expensive probes because the distance of the probe from the surface of the object is optimized in such a way as to consequently minimize also the required measurement band. In this way it is also possible to use more precise probes. Furthermore, the acquisition of points on the surface of the object can be made in correspondence with predetermined points, thus reducing the quantity of information which is transferred to the processing system associated with the probe.
If, on the other hand, the system of this invention is integrated into the known xe2x80x9cpoint cloudxe2x80x9d acquisition systems, the numerical model of the resulting surface is accurate and easy to obtain, and does not involve an excessive load of numerical processing on the data of the point clouds.
In general, however, the system of this invention makes it possible to process optimized paths for the detection of points on the actual model, according to the characteristics of the probe used. For example, it is known that the non-contact fixed-focus known type of probes are able to correctly detect points on a surface whose perpendicular has an inclination with respect to a predetermined axial direction of the probe within around 20xc2x0-30xc2x0. The optimization of the paths makes it possible to group in one or more homogeneous groups all the theoretical points in which the perpendiculars with respect to the theoretical surface passing through these points present directions within a predetermined spherical angle, preferably around 40xc2x0-60xc2x0. This makes it possible to notably reduce the acquisition time of points on an actual surface, which is significantly affected by the probe re-orientation times to modify its predetermined axial direction. Naturally, what is said above regarding the optimization of the acquisition paths of non-contact fixed-focus probes, also applies to any other type of probe, for example the non-contact measurement band type and the traditional contact type.